In a MC framework, the most common scheme employed in the industry is the Euler-Maruyama discretization of the system of SDEs which describe the underlying process dynamics. For the the stochastic volatility model of Heston, such scheme can be improved, allowing for an exact simulation of the variance process \(v(t)\)  (see ()), as shown in [1]}. This results in increased accuracy, and avoids numerical issues due to the theoretical non-negativity of the process \(v(t)\) , leading to the so-called almost exact simulation of the Heston model [2]}.
